Doubtful. Early numbers are showing the birth rates are tanking in red states. Most of the white women there are also poor. Well off white women can still travel for reproductive healthcare.
It might have gone the way you described. After all, most of these women are also religious and it IS religion pushing this ridiculousness.
But nobody wants to have a baby without medical care. We all know what the stata were before modern medical care and how horrific sepsis deaths and other post partum mortalities are.
Driving off all the doctors was a dumb ass move. Threatening birth control so soon after their Dobbs victory, also a dumb ass move.
A lot of young women are talking about taking on an extra job or skipping a semester of school and travellint out of state or country to get sterilized.
Joining the service is another way to get it done without all the hassle, but I haven't heard much talk about that yet. Great recruitment point though.
I guess time will tell